The posts on the site referred to are neither comprehensive nor really helpful.

This is a request to find the range of x and y values to satisfy two inequalities simultaneously. I think the best way to understand the question is to look at it graphically.

Plot the equation for x+y=4Then the inequality x+y<4 is satisfied by points on one side of the line. The origin is such a point. So all points on the same side of the line as the origin satisfy the inequality.

Next plot -2x+3y=9Again the origin satisfies the inequality, so all points on the same side of the line as the origin satisfy the inequality.

The two lines intersect at x=3/5, y= 17/5

This value of y is the greatest y value for which both inequalities are satisfied simultaneously. And it is only true if x=3/5

If y=0 then both inequalities are satisfied if -9/2<x<4

And similarly for any other value of y<17/5

You asked about corner points. There is really only one relevant corner: x=3/5, y=17/5